Effects of Relugolix vs Leuprolide on Cardiac Function in Patients With Prostate Cancer

Inclusion Criteria: * Pathologically proven diagnosis of adenocarcinoma of the prostate within 270 days prior to registration. * Unfavorable intermediate risk prostate cancer, defined as having ALL the following bulleted criteria: * Has at least one intermediate risk factor (IRF): * Prostate-specific antigen (PSA) 10-20 ng/mL * Clinical stage tumor (T)2b-c (digital rectal exam \[DRE\] and/or imaging) by American Joint Committee on Cancer (AJCC) 8th edition * Gleason Score 7 (Gleason 3+4 or 4+3 \[International Society of Urological Pathology \[ISUP\] grade group 2-3\]) * Has one or more of the following "unfavorable" intermediate-risk designators: * \> 1 IRF * Gleason 4+3=7 (ISUP grade group 3) * ≥ 50% of biopsy cores positive * Biopsies may include "sextant" sampling of right/left regions of the prostate, often labeled base, mid-gland and apex. All such "sextant" biopsy cores should be counted. Men may also undergo "targeted" sampling of prostate lesions (guided by MRI, ultrasound or other approaches). A targeted lesion that is biopsied more than once and demonstrates cancer (regardless of number of targeted cores involved) should count as a single additional positive core sampled and positive. In cases of uncertainty, count the biopsy sampling as sextant core(s). * Absence of high-risk features * Appropriate stage based on the following diagnostic workup: * History/physical examination within 120 days prior to registration * Negative bone imaging (M0) with Tc-99m bone scan or fluciclovine (18F) sodium fluoride (NaF) positron emission tomography (PET) within 120 days prior to registration * Clinically negative lymph nodes (N0) as established by conventional imaging (pelvic +/- abdominal CT or MRI), within 120 days prior to registration (lymph nodes equivocal or questionable by imaging are eligible if the nodes are ≤ 1.0 cm in short axis and/or if biopsy is negative) * Prostate specific membrane antigen (PSMA) or fluciclovine PET negative for nodal or distant metastatic disease is an acceptable substitute for the above bone and pelvic imaging * Age ≥ 18 * Eastern Cooperative Oncology Group (ECOG) Performance Status of 0-1 within 120 days prior to registration. * Non-castrate testosterone level (\> 50 ng/dL) within 120 days prior to registration. * Absolute neutrophil ≥ 1,000 cells/mm\^3 (within 120 days prior to registration) * Hemoglobin ≥ 10 g/dL (within 120 days prior to registration) * Platelet count ≥ 100,000 cells/mm\^3 (within 120 days prior to registration) * Creatinine clearance (CrCl) ≥ 30 mL/min estimated by Cockcroft-Gault Equation (within 120 days prior to registration) * For African American patients, CrCl ≥ 30 mL/min is estimated by the alternative formula that takes race into account * Total bilirubin: 1.5 ≤ institutional upper limit of normal (ULN) (within 120 days prior to registration) * Aspartate aminotransferase (AST)(serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT)(serum glutamic-pyruvic transaminase \[SGPT\]) ≤ 2.5 × institutional ULN (within 120 days prior to registration) * HIV-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial. Note: HIV testing is not required for eligibility for this protocol. * For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated. Note: Known positive test for hepatitis B virus surface antigen (HBV sAg) indicating acute or chronic infection would make the patient ineligible unless the viral load becomes undetectable on suppressive therapy. Patients who are immune to hepatitis B (anti-Hepatitis B surface antibody positive) are eligible (e.g. patients immunized against hepatitis B). * For patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load. * Note: Known positive test for hepatitis C virus ribonucleic acid (HCV RNA) indicating acute or chronic infection would make the patient ineligible unless the viral load becomes undetectable on suppressive therapy. * The patient or a legally authorized representative must provide study-specific informed consent prior to study entry and, for patients treated in the United States (U.S.), authorization permitting release of personal health information. Exclusion Criteria: * Previous radical surgery (prostatectomy) or any form of curative-intent ablation whether focal or whole-gland (e.g., cryosurgery, High-intensity focused ultrasound (HIFU), laser thermal ablation, etc.) for prostate cancer. * Definitive clinical or radiologic evidence of metastatic disease (M1). * Prior invasive malignancy (except non-melanomatous skin cancer) or hematologic malignancy unless disease free for a minimum of 3 years. * Prior radiotherapy to the prostate/pelvis region that would result in overlap of radiation therapy fields. * Previous bilateral orchiectomy. * Previous hormonal therapy, such as luteinizing hormone-releasing hormone (LHRH) agonists (e.g., leuprolide, goserelin, buserelin, triptorelin) or LHRH antagonist (e.g. degarelix), anti-androgens (e.g., flutamide, bicalutamide, cyproterone acetate). ADT started prior to study registration is not allowed. * Prior use of 5-alpha-reductase inhibitors is allowed; however, it must be stopped ≥ 30 days prior to the pre-registration PSA measure for determining enrollment eligibility. * Prior testosterone replacement therapy is allowed; however, any replacement therapy must be stopped for at least 1 year prior to registration. * Severe, active co-morbidity defined as follows: * Current/uncontrolled angina or arrhythmias * New York Heart Association Functional Classification II-IV (Note: Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification.) * History of any condition that in the opinion of the investigator, would preclude participation in this study * Patients with significant obstructive urinary symptoms that are suspected to be secondary to prostate cancer and/or benign prostatic hypertrophy. * Disabilities that prevent performing moderate intensity exercise test with exercise (treadmill) stress test and muscle function tests (walking/gait assessments and grip strength). * Patients unable to tolerate MRI (e.g. claustrophobia), has contraindications to MRI (e.g. metals and implants incompatible with MRI), body habitus preventing MRI scanning, or allergy to gadolinium-based contrast. * Significant uncontrolled gastrointestinal (e.g. Crohn's disease, ulcerative colitis) or metabolic disease (e.g. diabetes, hyperlipidemia). * Active inflammatory or immune-related disease treated with steroids or immunosuppressive agents. * Inability to swallow oral pills. * High risk features, which includes any of the following: * Gleason 8-10 \[ISUP grade group 4-5\] * PSA\>20 * cT3-4 by digital exam OR gross extra-prostatic extension on imaging \[indeterminate MRI evidence will not count and the patient will be eligible\]